# Optimal Transport and Tessellation - Mathematics > Probability

Abstract: Optimal transport from the volume measure to a convex combination of Diracmeasures yields a tessellation of a Riemannian manifold into pieces ofarbitrary relative size. This tessellation is studied for the cost functions$c pz,y=\frac{1}{p}d^pz,y$ and $1\leq p<\infty$. Geometric descriptions ofthe tessellations for all $p$ is obtained for compact subsets of the Euclideanspace. For $p=2$ this approach yields Laguerre tessellations. For $p=1$ itinduces Johnson Mehl diagrams for all compact Riemannian manifolds.

Author: Martin Huesmann

Source: https://arxiv.org/